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^{2}+14x+5)/[(x+1)

^{2}(2x+1)] does it have to be split into three partial fractions, A/(x+1) + B/(x+1)

^{2}+ C/(2x+1)?

When my first saw this example, my initial reaction was to split it into A/(x+1)

^{2}+B/(2x+1), but after working through this, I realised my method was wrong. Why doesn't it work? I don't want a worked answer to the example because I already know what it is. I just want a genuine logical reason to why the former works and the latter doesn't.

Thanks :)